{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch as th\n",
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sy\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x,y):\n",
    "  return (1-x/2 + x**5 + y**3) * np.exp(-x**2 - y**2)\n",
    "\n",
    "def df(x,y):\n",
    "  dfx = -2 * x * f(x,y) + (5 * x**4 - 1/2) * np.exp(-x**2 - y**2)\n",
    "  dfy = -2 * y * f(x,y) + 3 * y**2 * np.exp(-x**2 - y**2)\n",
    "  return  dfx,dfy\n",
    "\n",
    "def flambda(lamb,x0,df0):\n",
    "    x = x0 + lamb * df0 \n",
    "    return f(x[0],x[1])\n",
    "\n",
    "def solve_lambda(x0):\n",
    "    df0 = df(x0[0],x0[1])\n",
    "    lamb = minimize(flambda,x0=1.0,args=(x0,df0))\n",
    "    return lamb.x,df0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3 y^{2} e^{- x^{2} - y^{2}} - 2 y \\left(x^{5} - \\frac{x}{2} + y^{3} + 1\\right) e^{- x^{2} - y^{2}}$"
      ],
      "text/plain": [
       "3*y**2*exp(-x**2 - y**2) - 2*y*(x**5 - x/2 + y**3 + 1)*exp(-x**2 - y**2)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x,y= sy.symbols(\"x,y\")\n",
    "\n",
    "z = (1-x/2 + x**5 + y**3) * sy.exp(-x**2 - y**2)\n",
    "\n",
    "z.diff(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x7ff8144064d0>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 256\n",
    "x = np.linspace(-5,5,n)\n",
    "y = np.linspace(-5,5,n)\n",
    "X,Y = np.meshgrid(x,y)\n",
    "fig=plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.contour(X,Y,f(X,Y),100)\n",
    "\n",
    "x0 = np.array([1,2])\n",
    "for i in range(4):\n",
    "  lamb,df0 = solve_lambda(x0)\n",
    "  ax.quiver(x0[0],x0[1],lamb*df0[0],lamb*df0[1],angles=\"xy\",scale_units=\"xy\",scale=1)\n",
    "  x0 = x0 + lamb*df0\n",
    "ax.grid()\n",
    "\n",
    "ax2 = fig.add_subplot(122,projection='3d')\n",
    "ax2.plot_surface(X,Y,f(X,Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-26.00872001])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lamb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.36744087, -0.7785065 ])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "newx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "f048195d803dbb89568bc164ee3edc71708837990e1fb62ab8e9fbba2f16c3ed"
  },
  "kernelspec": {
   "display_name": "Python 3.7.6 64-bit ('base': conda)",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
